Challenges in applying quantum optimization to agent-based modeling: A Schelling segregation case study

Quantum computing promises transformative advances, but recurring misconceptions and methodological pitfalls limit progress. This paper examines challenges that arise when traditional agent-based modeling implementations are directly mapped to quantum optimization frameworks like quadratic unconstrained binary optimization. Using Schelling’s segregation model as a case study, we show that directly translating agent-based modeling state observations into quadratic unconstrained binary optimization formulations not only fails to deliver quantum advantage, but also actively undermines computational efficiency. The fundamental issue is architectural. Traditional agent-based modeling frameworks observe the complete system state at each iteration, which can destroy quantum superposition. This motivates reconsidering the computational structure when seeking quantum advantage. Through analysis of Schelling’s segregation dynamics on lollipop networks, we demonstrate that abandoning the quadratic unconstrained binary optimization reduction paradigm and reconceptualizing the research question—from “simulate agent dynamics iteratively until convergence” to “compute the minimum number of agent moves required for global satisfaction”—enables a faster classical solution. This structural reconceptualization yields an algorithm that exploits network symmetries obscured in traditional agent-based modeling simulations and quadratic unconstrained binary optimization formulations. It establishes an algorithmic lower bound of O(n) for the decision problem on lollipop networks, which any quantum approach must outperform to achieve advantage. This result also extends the equilibrium characterization of Schelling’s model across various graph structures. Our work emphasizes that progress in quantum agent-based modeling should not force classical implementations into quantum frameworks. Instead, it should focus on clarifying when quantum advantage is structurally possible, developing best-in-class classical baselines, and fundamentally reformulating research questions rather than preserving classical iterative paradigms.